The present invention relates to a method and a device for measuring dielectric constants by microwaves, of sheetlike substances such as a high-polymer sheet and paper including film, and three-dimensional articles such as moldings of plastic, resin, rubber and the like, as well as liquids such as an aqueous solution, a water dispersion liquid, an organic solvent liquid, liquid organic matter and the like.
A dielectric constant is a physical value based on polarization in the inner part of a substance similar to a refractive index, and considered as an important physical value since the same is closely connected with electric, optical and dynamic physical properties. In a high-frequency domain such as light, the refractive index and the dielectric constant are in the relation:
(refractive index)2=dielectric constant
and, hence, it is also possible to make substitution by either one as the case may be. For a transparent substance, refractive index measurement by a refractive index meter is frequently employed. For a flat plate sample, various methods such as a method of obtaining the dielectric constant from the capacity of a plate capacitor, a method according to a microwave cavity resonator or a dielectric resonator and the like have been employed.
A method employing resonance of microwaves, utilizing such a principle that a resonance frequency shifts in correspondence to the dielectric constant, is directed to paper, a film, plastic, ceramic and rubber etc., and can be utilized regardless of presence/absence of optical transparency.
FIG. 1 illustrates a principle diagram of conventional dielectric constant measurement employing a microwave cavity resonator. It is a microwave resonator 6 comprising a microwave introduction part 2 on an end and a microwave sensing part 4 on another end while a portion between both end portions consists of a waveguide having a constant field vibrational direction. A slit 8 is provided on the resonator 6 in a direction perpendicularly crossing the axis of the resonator 6 on the position of a loop of standing waves. A sample 10 is arranged in the slit 8 and microwaves are introduced from the microwave introduction part 2, for detecting the microwave intensity by the microwave sensing part 4. The dielectric constant is measured from the amount of displacement between a resonance frequency without arranging the sample 10 in the slit 8 and a resonance frequency at the time of not arranging the sample (refer to Japanese Patent Publication Gazette No. 3-38632).
A method of measuring a dielectric constant with microwave dielectric resonators is shown in FIG. 2. FIG. 2 is a sectional view showing a conventional orientation measuring device employing dielectric resonators. Referring to the figure, it comprises a pair of dielectric resonators 12a and 12b opposed through a sample 10, for making the dielectric resonators 12a and 12b generate field vectors having a single direction parallel to the surface of the sample 10 by a pair of antennas 14a and 14b oppositely arranged on side portions of the first dielectric resonator 12a through the dielectric resonator 12a and measuring the dielectric constant from the resonance characteristics thereof (refer to Japanese Utility Model Laying-Open Gazette No. 3-70368). Here, the antennas 14a and 14b are in the form of loops.
In the measuring device shown in FIG. 1 or FIG. 2, the cavity resonator or the dielectric resonators hold the sample 10 and are oppositely arranged on both sides thereof, and hence the shape of the measured sample 10 is limited to a sheetlike one. However, in the recent plastic molding field, the necessity for measuring the dielectric constant of molded plastic or its anisotropy has become strong. For example, in a resin molding of an electrical appliance such as a PC and a television set, or a plastic vessel such as a PET bottle, the dielectric constant or its anisotropy remarkably varies with positions due to flowability distribution, pressure distribution or the like in molding, which has come into question. Therefore, measurement of the dielectric constant or its anisotropy of a three-dimensional article is in demand.
The refractive index of a liquid is currently measured by an optical method, and the sugar level of fruit juice, the degree of fatigue of oil, the concentration of soy sauce or the like may also be managed with this refractive index. However, with this method, there is a problem that it is difficult to measure an opaque liquid such as heavy oil that can hardly transmit light There is also such a problem that only a substance of which refractive index is up to 1.52 at the maximum can be measured by the optical method from a critical angle in total reflection of light
An object of the present invention is to make it possible to measure dielectric constants not only in a sheetlike sample but also in a sample such as a three-dimensional molding and a liquid sample.
An aspect of a dielectric constant measuring method according to the present invention includes the following steps:
(step 1) a step of arranging a sample measuring face of a single dielectric resonator arranged only on one side of a sample under a fixed condition on a standard sample of which dielectric constant is known, properly varying either one or both (referred to as xe2x80x9cthe dielectric constant and/or the thicknessxe2x80x9d) of the dielectric constant and the thickness of the standard sample for measuring a variance in the resonance frequency of the dielectric resonator with respect to each dielectric constant and/or thickness and acquiring a calibration curve in the variance of the resonance frequency responsive to the dielectric constant and/or the thickness.
(step 2) a step of measuring a variance of the resonance frequency by the dielectric resonator under the fixed condition as to a measured object sample of which the thickness is known.
(step 3) a step of obtaining the dielectric constant of the measured object sample from the measured value. and the calibration curve.
Another aspect of the dielectric constant measuring method is a dielectric constant measuring method arranging a sample measuring face of a single dielectric resonator arranged only on one side of a sample under a fixed condition on a measured object sample of which the thickness is. known, measuring a resonance frequency and obtaining the dielectric constant of the measured object sample according to the following equation (1):
xcex2gL32 xcfx80/2+Pxcfx80+tanxe2x88x921(xcex12/xcex2g)xc2x7tan h[tan hxe2x88x921(xcex13/xcex12)+xcex12L2]xe2x80x83xe2x80x83(1)
xcex12=(kc2xe2x88x92xcfx8902xcex50xcexc0xcex5s)xc2xd
xcex13=(kc2xe2x88x92xcfx8902xcex50xcexc0)xc2xd
xcex2g=(xcfx8902xcex50xcexc0xcex5rxe2x88x92kc2)xc2xd
where xcex5s represents the dielectric constant of the sample, xcex5r represents the relative dielectric constant of the dielectric resonator, L represents the thickness of the dielectric resonator, xcex50 represents the dielectric constant of a measuring atmosphere. (air), xcexc0 represents the magnetic permeability of the measuring atmosphere, xcfx890 represents a microwave resonance angular frequency, L2 represents the thickness of the measured object sample, kc represents a constant (eigenvalue) determined by the shape of the dielectric resonator, an electromagnetic field mode or the like, and P represents 0, 1, 2, 3, . . . (these numerals mean integral times xcexg/2 in the axial direction).
Here, xe2x80x9ca fixed conditionxe2x80x9d refers to operation of performing measurement while bringing the sample measuring face of the dielectric resonator into contact with the sample, or performing measurement while separating the sample measuring face of the dielectric resonator from the sample by a fixed distance.
In the dielectric constant measuring method according to the present invention, the resonance mode of the dielectric resonator is preferably such a mode that evanescent waves exude from the inner part of the dielectric resonator by resonance onto the side of the sample measuring face of the dielectric resonator.
If it is such a mode that field vectors of the evanescent waves are substantially parallel to one direction in such a resonance mode, the dielectric constant of the sample in the parallel direction can be measured.
In the dielectric constant measuring method according to the present invention, it is possible to use a cylindrical resonator and also to use a square resonator as the dielectric resonator.
In the dielectric constant measuring method according to the present invention, such a structure can be preferably employed that antennas of an exciter and a detector of the dielectric resonator are stick-shaped rod antennas arranged in a direction perpendicular to the sample measuring face of the dielectric resonator, the sample measuring face being close to or in contact with the sample.
In the aforementioned dielectric constant measuring method, such a structure can be preferably employed that the periphery of the dielectric resonator is covered with a shielding vessel except the sample measuring face.
In the aforementioned dielectric constant measuring method, the measurement sample can be measured also when the same is a liquid.
A dielectric constant measuring device according to the present invention comprises a single dielectric resonator arranged only on one side of a sample, a memory device made to store a calibration curve as to a variance of a resonance frequency measured by the dielectric resonator with respect to each thickness while varying the thickness of a standard sample of which dielectric constant is known and a data processor operating the dielectric constant of a measured object sample from a result of measurement of the variance of the resonance frequency of the measured object sample and the calibration curve.
[Measurement Principle]
FIG. 3 is a general model diagram in a case of bringing a sample 10 into contact with a dielectric resonator 20. According to this figure, schematic description is now made with reference to an electromagnetic field mode mainly used for measurement in a case of expressing the. resonance state of a dielectric resonator in a numerical formula. Assuming that dielectric substances of the dielectric resonator and the sample have no loss, a resonance frequency f0 is obtained from xcfx890=2xcfx80f0 satisfying the following equation:
xcex2gL=xcfx80/2+Pxcfx80+tanxe2x88x921(xcex13/xcex2g)xc2x7tan h[{tan hxe2x88x921(xcex13/xcex12)xc2x7cot hxcex13L3}+xcex12L2]xe2x80x83xe2x80x83(A)
xcex12, xcex13 and xcex2g represent constants in a case of employing each area as a waveguide, while xcex12 and xcex13 are damping coefficients and xcex2g is a phase constant, which are expressed as follows:
xcex12=(kc2xe2x88x92xcfx8902xcex50xcexc0xcex5s)xc2xd
xcex13=(kc2xe2x88x92xcfx8902xcex50xcexc0)xc2xd
xcex2g=(xcfx8902xcex50xcexc0xcex5rxe2x88x92kc2)xc2xd
where xcex5s represents the dielectric constant of the sample, xcex5r represents the relative dielectric constant of the dielectric resonator, L represents the thickness of the dielectric resonator, xcex50 represents the dielectric constant of a measuring atmosphere (air), xcexc0 represents the magnetic permeability of the measuring atmosphere, xcfx890 represents a microwave resonance angular frequency, L2 represents the thickness of the measured object sample, kc represents a constant (eigenvalue) determined by the shape of the dielectric resonator, an electromagnetic field mode or the like, and P represents 0, 1, 2, 3, . . . (these numerals mean integral times xcexg/2 in the axial direction). kc, which is determined by the shape of the dielectric resonator, the electromagnetic field mode, or the like, becomes as follows when the length and the width are xe2x80x9caxe2x80x9d and xe2x80x9cbxe2x80x9d if the same can be regarded as a square magnetic wall:
kcmn2=(mxcfx80/a)2+(nxcfx80/b)2
xe2x80x9cmxe2x80x9d and xe2x80x9cnxe2x80x9d represent 0, 1, 2, 3, . . . (these numerals mean integral times xcex/2 in the sectional direction).
In the above equation (A), the measuring atmosphere is generally in the air in measurement, and an electric wall rightward beyond the measured object in the figure may be regarded as being at infinity, whereby coth xcex13L3xe2x86x921 in the case of L3xe2x86x92∞, and an equation (1) is obtained from the above equation (A).
xe2x80x83xcex2gL=xcfx80/2+Pxcfx80+tanxe2x88x921(xcex12/xcex2g)xc2x7tan h[tan hxe2x88x921(xcex13/xcex12)+xcex12L2]xe2x80x83xe2x80x83(1)
It is understood from the above relation that the resonance frequency varies if the dielectric constant xcex5s of the sample or the thickness L2 of the sample changes. That is, it indicates that the shifting quantity of the resonance frequency increases as compared with a blank time (where there is no measured sample) as the dielectric constant xcex5s increases and the shifting quantity increases as the thickness L2 increases. However, the strength of field vectors is at the maximum on the surface of the dielectric resonator and exponentially decreases as separating therefrom since evanescent waves are employed.
When solving this equation (1) in practice, it is easily obtained through a personal computer when mathematical software such as mathematical software sold under the trademark MATHEMATICA(copyright), a U.S. registered trademark owned by Wolfram Research, Inc. of Champaign, Ill., is used. A measurement result having a small number of errors can be obtained by properly combining the aforementioned method of solving the equation and actually obtained calibration curve data.
While the above equation has been described with reference to the case of bringing the sample 10 into contact with the dielectric resonator 20, an equation is almost similarly obtained also when measuring the sample at a fixed interval from the sample measuring face of the dielectric resonator.
Therefore, when investigating the relation between the difference (assumed to be xcex94f) between the resonance frequency at the blank time and the resonance frequency at the time when the sample is arranged and forming a calibration curve, it follows that the dielectric constant of the sample can be measured merely by measuring the thickness and xcex94f. Also, depending on conditions, the dielectric constant of the sample can be obtained by solving the above equation (1).
FIG. 4 shows a block structural diagram of a measuring system of one Example of the present invention. It comprises a dielectric resonator 20 having a plane close to or in contact with a sample 10, a shielding vessel 26 substantially covering the dielectric resonator 20 except its sample measuring face, a microwave exciter 15 generating a frequency close to the resonance frequency of the dielectric resonator 20 at the time when the sample is present from an antenna 22a, a detector 16 detecting transmitted energy or reflected energy by the dielectric resonator 20 through an antenna 22b, a resonance frequency sensor 17 obtaining the resonance frequency from a variance of an output of the detector 16, and a computer 18 which is a data processor obtaining the dielectric constant of the sample 10 from the obtained resonance frequency. The computer 18 has a memory device 19 storing previously obtained calibration curve data or the like.
Microwaves are sent from the exciter 15 enabled to continuously vary the microwave frequency over a certain frequency range around the resonance frequency to the dielectric resonator 20, and the transmitted microwave intensity is sensed by the detector 16. This signal is sent to the resonance frequency sensor 17 in which the resonance frequency is measured, and this is sent to the computer 18. Calibration curve data of various dielectric constants and sample thicknesses are stored in the memory device 19, and the dielectric constant of the sample 10 is calculated from the calibration curve data and the measured resonance frequency by an extrapolation operation or the like.
While an example using calibration curve data has been described with reference to the above example, the dielectric constant of the sample can also be obtained by an operation by solving the equation (1) with the computer 18. In this case, it is also possible to obtain the dielectric constant of the sample while reducing errors in the operation process for the equation (1) with the calibration curve data.
While the antennas of the microwave exciter and the detector may be those in the forms of loops or rods, stick-shaped rod-shaped ones are. superior in homogeneity of field vectors in the in-sample plane and, hence, more preferable than loop-shaped ones as the antennas when the dielectric resonator are squared. At this time, the rod-shaped antennas are preferably arranged in a direction perpendicular to a plane of the dielectric resonator, the plane being close to or in contact with the sample.
[Embodiment 1 of the Invention]
FIG. 5 shows structural diagrams of a dielectric resonator according to one Example of the present invention. It follows that the dielectric resonator 20 is connected to the measuring system shown in FIG. 4. When detecting transmitted energy by the detector, the exciter and the detector are connected to the respective ones of the pair of antennas 22a and 22b oppositely arranged through the dielectric resonator 20.
FIG. 5 shows a sectional view (a) of an exemplary dielectric resonator including antennas and a top plan view (b) thereof. Referring to the figure, the microwave rod antennas (or loop antennas) 22a and 22b are arranged on positions and in a direction shown in the figure with respect to the dielectric resonator 20, so that the dielectric resonator 20 can be resonated while such a resonance mode can be formed that there are field vectors exuding outward from the dielectric resonator 20. While there is a TM mode, a TE mode and the like as the resonance mode, FIG. 5 expresses a TM101, mode. While the strength of field vectors 24 almost exponentially decreases as separating from the dielectric resonator 20, the sample is placed at a short distance from the dielectric resonator 20 or in contact with the dielectric resonator 20 so that the resonance frequency shifts by electromagnetic coupling in response to the dielectric constant of the sample.
Because the field vectors become parallel on the dielectric surface and in the inner part of the sample in the case of this resonance mode, it becomes possible to measure the dielectric constant in the direction of the vectors. Therefore, anisotropy of the dielectric constant on the position can also be measured by turning the dielectric resonator 20 at a set angle around a rotation axis perpendicular to the sample surface using some sort of method and measuring the dielectric constant at each time.
The aforementioned arrangement, shapes etc. of the microwave rod antennas (or loop antennas) 22a and 22b with respect to the dielectric resonator 20 are not restricted to these but any arrangement and shapes may be employed so far as the dielectric resonator 20 can be resonated and such a resonance mode can be formed that there are field vectors exuding outward from the dielectric resonator 2. In the Example of FIG. 5, a square resonator is used for the dielectric resonator 20, and the rod antennas 22a and 22b are used as the antennas. Field vectors having the most excellent homogeneity can be obtained by thus combining a square resonator and rod antennas.
The periphery of the dielectric resonator 20 is preferably covered with the shielding vessel 26 except the sample measuring face in consideration of improvement in sensitivity etc. Thus, the Q value of a resonance curve can be increased. The shielding vessel is generally made of a conductive material such as a metal.
[Embodiment 2 of the Invention]
When there is no need to obtain information of anisotropy of a dielectric constant, i.e., when an average dielectric constant of a sample is to be measured dissimilarly to the example described in the embodiment 1 of the present invention, it is preferable to employ not a square but cylindrical dielectric resonator. The positions and the direction of mounting antennas are taken into consideration thereby making resonance, e.g., in a TE01xcex4 or HEM21xcex4 mode to enter such a field mode that exuding evanescent waves are in the form of a loop or not unidirectionally biased as shown in FIG. 6 on the sample surface, and the average dielectric constant can be measured. FIG. 6 is a diagram showing field distribution on the dielectric resonator surface in the HEM21xcex4 mode in the case of requiring no measurement of anisotropy, and a circle shown by a solid line in the figure shows the upper surface of the cylindrical dielectric resonator.
The present invention utilizes the evanescent waves exuding outward from the dielectric resonator in the aforementioned manner, for measuring the dielectric constant
[Embodiment 3 of the Invention]
It has been considered effective to further increase sharpness (Q value) of resonance in the first place for sharpening a resonance curve, in order to further improve the sensitivity of a dielectric resonator. Therefore, the inventors have made various trials.
Consequently, It has been found that it is effective to properly increase the distance between surfaces other than a sample measuring face and a shielding vessel. The optimum value thereof has also been found.
As to this value, the distance between the bottom surface (surface opposed to the sample measuring face) of the dielectric resonator and the shielding vessel was concretely 0.2 to 0.8 mm, preferably 0.3 to 0.6 mm. The distance between a side surface of the dielectric resonator and the shielding vessel was 2 to 5 mm, preferably 1 to 3 mm in the case of using a rod antenna as an antenna on the side surface not provided with the rod antenna. It was substantially similar also on the side surface provided with the rod antenna. However, it was more preferable that the distance on the side surface provided with the rod antenna was narrower than the distance on the side surface provided with no antenna. The above numerical values also depend on a used frequency and the dimensions of the dielectric resonator, and the degrees of the aforementioned values are conceivably preferable at the degrees of the bottom surface (30 mmxc3x9720 mm) and the height (20 mm) which are current dimensions. It is conceivably preferable to reduce the distances by more when these dimensions decrease by more or the used frequency exceeds the currently used degrees of gigahertz. In any case, it is preferable that the dielectric resonator and the shielding vessel are not in contact with each other.
It has been recognized that the Q value is remarkably improved by inserting a substance having a small dielectric loss factor such as polytetrafluoroethylene (PTFE) or quartz between the surfaces where the bottom surface (surface opposed to the sample measuring face) of the dielectric resonator opposed to the sample measuring face and the shielding vessel are opposed, to enable correct measurement of the resonance frequency. While it is preferable that the distances can be kept in such a state that the spacer is as small as possible or absent if possible, a flat plate of several mm square or a disk of several mm in diameter was used in practice.
It has also been recognized that the Q value is increased by optimizing the length of the rod antenna, and the distance to the dielectric resonator, etc.
Furthermore, as to preventing from intrusion of paper particles or liquid, it has been recognized that contamination with foreign matter can be prevented without substantially reducing the Q value by filling up a part or whole of a gap portion between the dielectric resonator and a metal with a substance (e.g., polytetrafluoroethylene) having a small dielectric constant and a small dielectric loss factor. Alternatively, it has also been recognized that a similar object can be attained also by covering the overall detection part with a thin sheet of a substance (e.g., polytetrafluoroethylene) similarly having a small dielectric constant and a small dielectric loss factor.
According to the present invention, the dielectric constant of the sample can be simply measured by merely measuring the resonance frequency when bringing the sample close to or in contact with the dielectric resonator.
This system is a sensing system from one side of the sample, whereby the measured sample does not have to be limited to a sheetlike dissimilarly to a conventional system, so even a thick block-shaped sample and a liquid sample can also be measured.